This chapter gives an overview of current research in evolutionary finance. We mainly focus on the survival and stability properties of investment strategies associated with the Kelly rule. Our approach to the study of the wealth dynamics of investment strategies is inspired by Darwinian ideas...

To analyze the economic significance of pricing errors of stock index options, a system of linear inequalities is developed which completely characterizes all risk arbitrage opportunities which arise if a well-behaved pricing kernel does not exist. The Stochastic Arbitrage system can account for...

I develop a portfolio choice model that allows for partial default and accommodates trade in a rich set of assets. I characterize the solution to an infinite horizon, consumption/portfolio problem with Markov shocks and many assets. The characterization facilitates a simple solution algorithm...

In recent years, academics, regulators, and market practitioners have increasingly addressed liquidity issues. Amongst the numerous problems addressed, the optimal execution of large orders is probably the one that has attracted the most research works, mainly in the case of single-asset...

Within a financial market where a risk-free bond and a long-lived risky asset are exchanged by investors with heterogeneous trading rules, we assume that the investors most exposed to the risky asset are subject to joint liquidation needs. The latter encompass a risk whenever the market impact...

In this paper, we solve a continuous-time portfolio choice problem of an investor under a Markov jump linear system that effectively captures stochasticity in asset returns, price impacts, and market resilience. Specifically, the investor chooses his portfolio to maximize the expected excess...

Measuring the performance of stock portfolios that include options is challenging due to options' nonlinearity in the underlying, their exposure to volatility risk, and their time decay. Our contribution to the literature is twofold: First, we provide a theoretically rigorous derivation of the...

We establish the existence and uniqueness of the equilibrium for a stochastic mean-field game of optimal investment. The analysis covers both finite and infinite time horizons, and the mean-field interaction of the representative company with a mass of identical and indistinguishable firms is...

This paper compares two well-known approaches for valuing a risky investment using real options theory:contingent claims (CC) with risk neutral valuation and dynamic programming (DP) using a constant risk adjusted discount rate.Both approaches have been used in valuing forest assets.A proof is...

We study the optimal consumption and investment choice for long-horizon investors with nontradable labor income and time-varying investment opportunities. Our results suggest that the popular investment recommendation that more conservative investors should hold a higher bond/stock ratio may...